The Catalan scholar Raymond Llull (1232–1315/16) constructed an intricate and complex system of diagrams that he hoped could be used for interreligious dialogue. His ultimate goal was that these figures, some of which included rotating disks, would help convince Jews and Muslims to convert to Christianity. However, Llull’s faith in the educational power of his diagrams was shaken when he had the opportunity to present them at the University of Paris, where the learned audience had difficulty understanding them. In his autobiography Via coaetanea (ca. 1311), Llull wrote that “because of the weakness of human intellect,” which he had witnessed in Paris, he had to simplify his diagrammatic system considerably. The weakness he had observed was not limited to Paris, the medieval era, or even to academic institutions; it is a general human trait. Throughout history, our cognitive limitations have, together with other fundamental aspects of cognition, constrained and shaped the development of diagrams. Interpreted through the lens of cognitive principles, the long trends and turning points in the history of diagrams can teach us valuable lessons about how humans construct and disseminate knowledge about the world.